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Mathematik-Online problems:

Problem 94: Definition and Determination of Limit


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Given the sequence $ (a_n)$ with

$\displaystyle a_n = \frac{1}{\sqrt{2n}-\sqrt{n}}\,. $

a)
Find $ {\displaystyle{a:=\lim_{n\to\infty} a_n}}$.
b)
Find for each constant $ \varepsilon=1$, $ \varepsilon=10^{-3}$ and $ \varepsilon=10^{-6}$ the smallest index $ n_0\in\mathbb{N}$, so that $ \vert a_n - a\vert < \varepsilon$, for all $ n > n_0$.

(Authors: Werner/Walk/Höfert)

see also:


[Solutions]

  automatisch erstellt am 14. 10. 2004